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Journal of High Energy Physics

, 2011:10 | Cite as

Scalar field propagation in the ϕ 4 κ-Minkowski model

  • S. Meljanac
  • A. Samsarov
  • J. Trampetić
  • M. Wohlgenannt
Article

Abstract

In this article we use the noncommutative (NC) κ-Minkowski ϕ 4 model based on the κ-deformed star product, (★ h ). The action is modified by expanding up to linear order in the κ-deformation parameter a, producing an effective model on commutative spacetime. For the computation of the tadpole diagram contributions to the scalar field propagation/self-energy, we anticipate that statistics on the κ-Minkowski is specifically κ-deformed. Thus our prescription in fact represents hybrid approach between standard quantum field theory (QFT) and NCQFT on the κ-deformed Minkowski spacetime, resulting in a κ-effective model. The propagation is analyzed in the framework of the two-point Green’s function for low, intermediate, and for the Planckian propagation energies, respectively. Semiclassical/hybrid behavior of the first order quantum correction do show up due to the κ-deformed momentum conservation law. For low energies, the dependence of the tadpole contribution on the deformation parameter a drops out completely, while for Planckian energies, it tends to a fixed finite value. The mass term of the scalar field is shifted and these shifts are very different at different propagation energies. At the Planck-ian energies we obtain the direction dependent κ-modified dispersion relations. Thus our κ-effective model for the massive scalar field shows a birefringence effect.

Keywords

Non-Commutative Geometry Field Theories in Higher Dimensions Renormalization Regularization and Renormalons 

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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • S. Meljanac
    • 1
  • A. Samsarov
    • 1
  • J. Trampetić
    • 1
    • 2
  • M. Wohlgenannt
    • 3
  1. 1.Rudjer Bošković InstituteZagrebCroatia
  2. 2.Max-Planck-Institut für Physik, (Werner-Heisenberg-Institut)MünchenGermany
  3. 3.Faculty of PhysicsUniversity of ViennaViennaAustria

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